Abstract

We report a theoretical and experimental study on the real and imaginary part of the third-order nonlinear optical susceptibility at 532 nm and 7 ns pulse for high-purity silica samples containing Au nanoparticles prepared by ion implantation. We present a method for measuring the magnitude and sign of refractive and absorptive nonlinearities based on four-wave mixing (FWM). This method is derived from a comparison of the light intensities of incident and self-diffracted polarized waves. In the nanosecond regime the samples exhibit saturable absorption and it seems that a thermal effect is the mechanism responsible of nonlinearity of index.

© 2007 Optical Society of America

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  1. S. S. Sarkisov, M. J. Curley, E. K. Williams, D. Ila, V. L. Svetchnikov, H. W. Zandbergen, G. A. Zykov, C. Banks, J. -C. Wang, D. B. Poker, and D. K. Hensley, "Nonlinear optical waveguides produced by MeV ion implantation in LiNbO3," Nucl. Instrum. Methods Phys. Res. B,  166-167, 750-757 (2000).
    [CrossRef]
  2. F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, "The optical Kerr effect in small metal particles and metal colloids: The case of gold," Appl. Phys. A 47, 347-357 (1988).
    [CrossRef]
  3. I. Tanahashi, Y. Manabe, T. Tohda, S. Sasaki, and A. Nakamura, "Optical nonlinearities of Au/SiO2 composite thin films prepared by a sputtering method," J. Appl. Phys. 79, 1244-1249 (1996).
    [CrossRef]
  4. H. B. Liao, R. F. Xiao, J. S. Fu, H. Wang, K. S. Wong, and G. K. L. Wong, "Origin of third-order optical nonlinearity in Au:SiO2 composite films on femtosecond and picosecond time scales," Opt. Lett. 23, 388-390 (1998).
    [CrossRef]
  5. F. Gonella and Mazzoldi, Handbook of Nanostructured Materials and Nanotechnology (Academic Press, San Diego), Vol. 4 (Optical properties), Chap. 2 (Metal nanoclusters composite glasses), (2000).
  6. J. C. Cheang-Wong, A. Oliver, A. Crespo-Sosa, J. M. Hernández, E. Muñoz, and R. Espejel-Morales, "Dependence of the optical properties on the ion implanted depth profiles in fused quartz after a sequential implantation with Si and Au ions" Nucl. Instrum. Methods Phys. Res. B 161-163, 1058-1063 (2000).
    [CrossRef]
  7. R. W. Boyd, Nonlinear Optics, (Academic Press, San Diego, 1992).
  8. M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, E. W. V. Stryland, "Sensitive measurement of optical nonlinearities using a single beam," IEEE J. Quantum Electron. 26, 760-769 (1990).
    [CrossRef]
  9. S. R. Friberg and P. W. Smith, "Nonlinear optical glasses for ultrafast optical switches," IEEE J. Quantum Electron. 23, 2089-2094 (1987).
    [CrossRef]
  10. P. D. Maker and R. W. Terhune, "Study of optical effects due to an induced polarization third order in electric field strength," Phys. Rev. 137, A801-A818 (1965).
    [CrossRef]
  11. M. J. Moran, C. Y. Shen, and R. L. Carman, "Interferometric measurement of nonlinear refractive-index coefficient relative to CS2 in laser-system related materials," IEEE J. Quantum Electron. 11, 259 (1975).
    [CrossRef]
  12. A. Owyoung, "Ellipse rotation studies in laser host materials," IEEE J. Quantum Electron. 9, 1064-1071 (1973).
    [CrossRef]
  13. R. Volle, V. Boucher, K. Dorkenoo, R. Chevalier, and X. Phu, "Local polarization state observation and third-order nonlinear susceptibility measurements by self-induced polarization state changes method," Opt. Commun. 182, 443-451 (2000).
    [CrossRef]
  14. K. Akihama, T. Asai, and S. Yamasaki, "Measurement method of nonresonant third-order susceptibility by using off-resonant coherent anti-Stokes Raman spectroscopy," Appl. Opt. 32, 7434-7441 (1993).
    [CrossRef] [PubMed]
  15. L. Rodríguez, C. Simos, M. Sylla, O. Marcano, and X. Phu, "New holographic technique for third-order optical properties measurement," Opt. Commun. 247, 453-460 (2005).
    [CrossRef]
  16. W. E. Williams, M. J. Soileau, and E. W. V Stryland, "Optical switching and n2 measurements in CS2," Opt. Commun. 50, 256-260 (1984).
    [CrossRef]
  17. Y. Bae, J. J. Song, and Y.B. Kim, "Photoacustic study of two-photon absorption in hexagonal ZnS," J. Appl. Phys. 53, 615-619 (1982).
    [CrossRef]
  18. I. Kang, T. Krauss, and F. Wise, "Sensitive measurement of nonlinear refraction and two-photon absorption by spectrally-resolved two-beam coupling," Opt. Lett. 22, 1077-1079 (1997).
    [CrossRef] [PubMed]
  19. A. Oliver, J. C. Cheang-Wong, J. Roiz, L. Rodríguez-Fernández, J. M. Hernández, A. Crespo-Sosa, E. Muñoz, "Metallic nanoparticle formation in ion-implanted silica after annealing in reducing or oxidizing atmospheres," Nucl. Instrum. Methods Phys. Res. B 191, 333-336 (2002).
    [CrossRef]
  20. C. Torres-Torres and A. V. Khomenko, "Vectorial self-diffraction of two degenerated waves in media with optical Kerr effect" (in Spanish), Revista Mex. de Física,  51, 162-167 (2005).

2005 (2)

L. Rodríguez, C. Simos, M. Sylla, O. Marcano, and X. Phu, "New holographic technique for third-order optical properties measurement," Opt. Commun. 247, 453-460 (2005).
[CrossRef]

C. Torres-Torres and A. V. Khomenko, "Vectorial self-diffraction of two degenerated waves in media with optical Kerr effect" (in Spanish), Revista Mex. de Física,  51, 162-167 (2005).

2002 (1)

A. Oliver, J. C. Cheang-Wong, J. Roiz, L. Rodríguez-Fernández, J. M. Hernández, A. Crespo-Sosa, E. Muñoz, "Metallic nanoparticle formation in ion-implanted silica after annealing in reducing or oxidizing atmospheres," Nucl. Instrum. Methods Phys. Res. B 191, 333-336 (2002).
[CrossRef]

2000 (3)

J. C. Cheang-Wong, A. Oliver, A. Crespo-Sosa, J. M. Hernández, E. Muñoz, and R. Espejel-Morales, "Dependence of the optical properties on the ion implanted depth profiles in fused quartz after a sequential implantation with Si and Au ions" Nucl. Instrum. Methods Phys. Res. B 161-163, 1058-1063 (2000).
[CrossRef]

R. Volle, V. Boucher, K. Dorkenoo, R. Chevalier, and X. Phu, "Local polarization state observation and third-order nonlinear susceptibility measurements by self-induced polarization state changes method," Opt. Commun. 182, 443-451 (2000).
[CrossRef]

S. S. Sarkisov, M. J. Curley, E. K. Williams, D. Ila, V. L. Svetchnikov, H. W. Zandbergen, G. A. Zykov, C. Banks, J. -C. Wang, D. B. Poker, and D. K. Hensley, "Nonlinear optical waveguides produced by MeV ion implantation in LiNbO3," Nucl. Instrum. Methods Phys. Res. B,  166-167, 750-757 (2000).
[CrossRef]

1998 (1)

1997 (1)

1996 (1)

I. Tanahashi, Y. Manabe, T. Tohda, S. Sasaki, and A. Nakamura, "Optical nonlinearities of Au/SiO2 composite thin films prepared by a sputtering method," J. Appl. Phys. 79, 1244-1249 (1996).
[CrossRef]

1993 (1)

1990 (1)

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, E. W. V. Stryland, "Sensitive measurement of optical nonlinearities using a single beam," IEEE J. Quantum Electron. 26, 760-769 (1990).
[CrossRef]

1988 (1)

F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, "The optical Kerr effect in small metal particles and metal colloids: The case of gold," Appl. Phys. A 47, 347-357 (1988).
[CrossRef]

1987 (1)

S. R. Friberg and P. W. Smith, "Nonlinear optical glasses for ultrafast optical switches," IEEE J. Quantum Electron. 23, 2089-2094 (1987).
[CrossRef]

1984 (1)

W. E. Williams, M. J. Soileau, and E. W. V Stryland, "Optical switching and n2 measurements in CS2," Opt. Commun. 50, 256-260 (1984).
[CrossRef]

1982 (1)

Y. Bae, J. J. Song, and Y.B. Kim, "Photoacustic study of two-photon absorption in hexagonal ZnS," J. Appl. Phys. 53, 615-619 (1982).
[CrossRef]

1975 (1)

M. J. Moran, C. Y. Shen, and R. L. Carman, "Interferometric measurement of nonlinear refractive-index coefficient relative to CS2 in laser-system related materials," IEEE J. Quantum Electron. 11, 259 (1975).
[CrossRef]

1973 (1)

A. Owyoung, "Ellipse rotation studies in laser host materials," IEEE J. Quantum Electron. 9, 1064-1071 (1973).
[CrossRef]

1965 (1)

P. D. Maker and R. W. Terhune, "Study of optical effects due to an induced polarization third order in electric field strength," Phys. Rev. 137, A801-A818 (1965).
[CrossRef]

Akihama, K.

Asai, T.

Bae, Y.

Y. Bae, J. J. Song, and Y.B. Kim, "Photoacustic study of two-photon absorption in hexagonal ZnS," J. Appl. Phys. 53, 615-619 (1982).
[CrossRef]

Banks, C.

S. S. Sarkisov, M. J. Curley, E. K. Williams, D. Ila, V. L. Svetchnikov, H. W. Zandbergen, G. A. Zykov, C. Banks, J. -C. Wang, D. B. Poker, and D. K. Hensley, "Nonlinear optical waveguides produced by MeV ion implantation in LiNbO3," Nucl. Instrum. Methods Phys. Res. B,  166-167, 750-757 (2000).
[CrossRef]

Boucher, V.

R. Volle, V. Boucher, K. Dorkenoo, R. Chevalier, and X. Phu, "Local polarization state observation and third-order nonlinear susceptibility measurements by self-induced polarization state changes method," Opt. Commun. 182, 443-451 (2000).
[CrossRef]

Carman, R. L.

M. J. Moran, C. Y. Shen, and R. L. Carman, "Interferometric measurement of nonlinear refractive-index coefficient relative to CS2 in laser-system related materials," IEEE J. Quantum Electron. 11, 259 (1975).
[CrossRef]

Cheang-Wong, J. C.

A. Oliver, J. C. Cheang-Wong, J. Roiz, L. Rodríguez-Fernández, J. M. Hernández, A. Crespo-Sosa, E. Muñoz, "Metallic nanoparticle formation in ion-implanted silica after annealing in reducing or oxidizing atmospheres," Nucl. Instrum. Methods Phys. Res. B 191, 333-336 (2002).
[CrossRef]

J. C. Cheang-Wong, A. Oliver, A. Crespo-Sosa, J. M. Hernández, E. Muñoz, and R. Espejel-Morales, "Dependence of the optical properties on the ion implanted depth profiles in fused quartz after a sequential implantation with Si and Au ions" Nucl. Instrum. Methods Phys. Res. B 161-163, 1058-1063 (2000).
[CrossRef]

Chevalier, R.

R. Volle, V. Boucher, K. Dorkenoo, R. Chevalier, and X. Phu, "Local polarization state observation and third-order nonlinear susceptibility measurements by self-induced polarization state changes method," Opt. Commun. 182, 443-451 (2000).
[CrossRef]

Crespo-Sosa, A.

A. Oliver, J. C. Cheang-Wong, J. Roiz, L. Rodríguez-Fernández, J. M. Hernández, A. Crespo-Sosa, E. Muñoz, "Metallic nanoparticle formation in ion-implanted silica after annealing in reducing or oxidizing atmospheres," Nucl. Instrum. Methods Phys. Res. B 191, 333-336 (2002).
[CrossRef]

J. C. Cheang-Wong, A. Oliver, A. Crespo-Sosa, J. M. Hernández, E. Muñoz, and R. Espejel-Morales, "Dependence of the optical properties on the ion implanted depth profiles in fused quartz after a sequential implantation with Si and Au ions" Nucl. Instrum. Methods Phys. Res. B 161-163, 1058-1063 (2000).
[CrossRef]

Curley, M. J.

S. S. Sarkisov, M. J. Curley, E. K. Williams, D. Ila, V. L. Svetchnikov, H. W. Zandbergen, G. A. Zykov, C. Banks, J. -C. Wang, D. B. Poker, and D. K. Hensley, "Nonlinear optical waveguides produced by MeV ion implantation in LiNbO3," Nucl. Instrum. Methods Phys. Res. B,  166-167, 750-757 (2000).
[CrossRef]

Dorkenoo, K.

R. Volle, V. Boucher, K. Dorkenoo, R. Chevalier, and X. Phu, "Local polarization state observation and third-order nonlinear susceptibility measurements by self-induced polarization state changes method," Opt. Commun. 182, 443-451 (2000).
[CrossRef]

Espejel-Morales, R.

J. C. Cheang-Wong, A. Oliver, A. Crespo-Sosa, J. M. Hernández, E. Muñoz, and R. Espejel-Morales, "Dependence of the optical properties on the ion implanted depth profiles in fused quartz after a sequential implantation with Si and Au ions" Nucl. Instrum. Methods Phys. Res. B 161-163, 1058-1063 (2000).
[CrossRef]

Flytzanis, C.

F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, "The optical Kerr effect in small metal particles and metal colloids: The case of gold," Appl. Phys. A 47, 347-357 (1988).
[CrossRef]

Friberg, S. R.

S. R. Friberg and P. W. Smith, "Nonlinear optical glasses for ultrafast optical switches," IEEE J. Quantum Electron. 23, 2089-2094 (1987).
[CrossRef]

Fu, J. S.

Hache, F.

F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, "The optical Kerr effect in small metal particles and metal colloids: The case of gold," Appl. Phys. A 47, 347-357 (1988).
[CrossRef]

Hagan, D. J.

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, E. W. V. Stryland, "Sensitive measurement of optical nonlinearities using a single beam," IEEE J. Quantum Electron. 26, 760-769 (1990).
[CrossRef]

Hensley, D. K.

S. S. Sarkisov, M. J. Curley, E. K. Williams, D. Ila, V. L. Svetchnikov, H. W. Zandbergen, G. A. Zykov, C. Banks, J. -C. Wang, D. B. Poker, and D. K. Hensley, "Nonlinear optical waveguides produced by MeV ion implantation in LiNbO3," Nucl. Instrum. Methods Phys. Res. B,  166-167, 750-757 (2000).
[CrossRef]

Hernández, J. M.

A. Oliver, J. C. Cheang-Wong, J. Roiz, L. Rodríguez-Fernández, J. M. Hernández, A. Crespo-Sosa, E. Muñoz, "Metallic nanoparticle formation in ion-implanted silica after annealing in reducing or oxidizing atmospheres," Nucl. Instrum. Methods Phys. Res. B 191, 333-336 (2002).
[CrossRef]

J. C. Cheang-Wong, A. Oliver, A. Crespo-Sosa, J. M. Hernández, E. Muñoz, and R. Espejel-Morales, "Dependence of the optical properties on the ion implanted depth profiles in fused quartz after a sequential implantation with Si and Au ions" Nucl. Instrum. Methods Phys. Res. B 161-163, 1058-1063 (2000).
[CrossRef]

Ila, D.

S. S. Sarkisov, M. J. Curley, E. K. Williams, D. Ila, V. L. Svetchnikov, H. W. Zandbergen, G. A. Zykov, C. Banks, J. -C. Wang, D. B. Poker, and D. K. Hensley, "Nonlinear optical waveguides produced by MeV ion implantation in LiNbO3," Nucl. Instrum. Methods Phys. Res. B,  166-167, 750-757 (2000).
[CrossRef]

Kang, I.

Khomenko, A. V.

C. Torres-Torres and A. V. Khomenko, "Vectorial self-diffraction of two degenerated waves in media with optical Kerr effect" (in Spanish), Revista Mex. de Física,  51, 162-167 (2005).

Kim, Y.B.

Y. Bae, J. J. Song, and Y.B. Kim, "Photoacustic study of two-photon absorption in hexagonal ZnS," J. Appl. Phys. 53, 615-619 (1982).
[CrossRef]

Krauss, T.

Kreibig, U.

F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, "The optical Kerr effect in small metal particles and metal colloids: The case of gold," Appl. Phys. A 47, 347-357 (1988).
[CrossRef]

Liao, H. B.

Maker, P. D.

P. D. Maker and R. W. Terhune, "Study of optical effects due to an induced polarization third order in electric field strength," Phys. Rev. 137, A801-A818 (1965).
[CrossRef]

Manabe, Y.

I. Tanahashi, Y. Manabe, T. Tohda, S. Sasaki, and A. Nakamura, "Optical nonlinearities of Au/SiO2 composite thin films prepared by a sputtering method," J. Appl. Phys. 79, 1244-1249 (1996).
[CrossRef]

Marcano, O.

L. Rodríguez, C. Simos, M. Sylla, O. Marcano, and X. Phu, "New holographic technique for third-order optical properties measurement," Opt. Commun. 247, 453-460 (2005).
[CrossRef]

Moran, M. J.

M. J. Moran, C. Y. Shen, and R. L. Carman, "Interferometric measurement of nonlinear refractive-index coefficient relative to CS2 in laser-system related materials," IEEE J. Quantum Electron. 11, 259 (1975).
[CrossRef]

Muñoz, E.

A. Oliver, J. C. Cheang-Wong, J. Roiz, L. Rodríguez-Fernández, J. M. Hernández, A. Crespo-Sosa, E. Muñoz, "Metallic nanoparticle formation in ion-implanted silica after annealing in reducing or oxidizing atmospheres," Nucl. Instrum. Methods Phys. Res. B 191, 333-336 (2002).
[CrossRef]

J. C. Cheang-Wong, A. Oliver, A. Crespo-Sosa, J. M. Hernández, E. Muñoz, and R. Espejel-Morales, "Dependence of the optical properties on the ion implanted depth profiles in fused quartz after a sequential implantation with Si and Au ions" Nucl. Instrum. Methods Phys. Res. B 161-163, 1058-1063 (2000).
[CrossRef]

Nakamura, A.

I. Tanahashi, Y. Manabe, T. Tohda, S. Sasaki, and A. Nakamura, "Optical nonlinearities of Au/SiO2 composite thin films prepared by a sputtering method," J. Appl. Phys. 79, 1244-1249 (1996).
[CrossRef]

Oliver, A.

A. Oliver, J. C. Cheang-Wong, J. Roiz, L. Rodríguez-Fernández, J. M. Hernández, A. Crespo-Sosa, E. Muñoz, "Metallic nanoparticle formation in ion-implanted silica after annealing in reducing or oxidizing atmospheres," Nucl. Instrum. Methods Phys. Res. B 191, 333-336 (2002).
[CrossRef]

J. C. Cheang-Wong, A. Oliver, A. Crespo-Sosa, J. M. Hernández, E. Muñoz, and R. Espejel-Morales, "Dependence of the optical properties on the ion implanted depth profiles in fused quartz after a sequential implantation with Si and Au ions" Nucl. Instrum. Methods Phys. Res. B 161-163, 1058-1063 (2000).
[CrossRef]

Owyoung, A.

A. Owyoung, "Ellipse rotation studies in laser host materials," IEEE J. Quantum Electron. 9, 1064-1071 (1973).
[CrossRef]

Phu, X.

L. Rodríguez, C. Simos, M. Sylla, O. Marcano, and X. Phu, "New holographic technique for third-order optical properties measurement," Opt. Commun. 247, 453-460 (2005).
[CrossRef]

R. Volle, V. Boucher, K. Dorkenoo, R. Chevalier, and X. Phu, "Local polarization state observation and third-order nonlinear susceptibility measurements by self-induced polarization state changes method," Opt. Commun. 182, 443-451 (2000).
[CrossRef]

Poker, D. B.

S. S. Sarkisov, M. J. Curley, E. K. Williams, D. Ila, V. L. Svetchnikov, H. W. Zandbergen, G. A. Zykov, C. Banks, J. -C. Wang, D. B. Poker, and D. K. Hensley, "Nonlinear optical waveguides produced by MeV ion implantation in LiNbO3," Nucl. Instrum. Methods Phys. Res. B,  166-167, 750-757 (2000).
[CrossRef]

Ricard, D.

F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, "The optical Kerr effect in small metal particles and metal colloids: The case of gold," Appl. Phys. A 47, 347-357 (1988).
[CrossRef]

Rodríguez, L.

L. Rodríguez, C. Simos, M. Sylla, O. Marcano, and X. Phu, "New holographic technique for third-order optical properties measurement," Opt. Commun. 247, 453-460 (2005).
[CrossRef]

Rodríguez-Fernández, L.

A. Oliver, J. C. Cheang-Wong, J. Roiz, L. Rodríguez-Fernández, J. M. Hernández, A. Crespo-Sosa, E. Muñoz, "Metallic nanoparticle formation in ion-implanted silica after annealing in reducing or oxidizing atmospheres," Nucl. Instrum. Methods Phys. Res. B 191, 333-336 (2002).
[CrossRef]

Roiz, J.

A. Oliver, J. C. Cheang-Wong, J. Roiz, L. Rodríguez-Fernández, J. M. Hernández, A. Crespo-Sosa, E. Muñoz, "Metallic nanoparticle formation in ion-implanted silica after annealing in reducing or oxidizing atmospheres," Nucl. Instrum. Methods Phys. Res. B 191, 333-336 (2002).
[CrossRef]

Said, A. A.

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, E. W. V. Stryland, "Sensitive measurement of optical nonlinearities using a single beam," IEEE J. Quantum Electron. 26, 760-769 (1990).
[CrossRef]

Sarkisov, S. S.

S. S. Sarkisov, M. J. Curley, E. K. Williams, D. Ila, V. L. Svetchnikov, H. W. Zandbergen, G. A. Zykov, C. Banks, J. -C. Wang, D. B. Poker, and D. K. Hensley, "Nonlinear optical waveguides produced by MeV ion implantation in LiNbO3," Nucl. Instrum. Methods Phys. Res. B,  166-167, 750-757 (2000).
[CrossRef]

Sasaki, S.

I. Tanahashi, Y. Manabe, T. Tohda, S. Sasaki, and A. Nakamura, "Optical nonlinearities of Au/SiO2 composite thin films prepared by a sputtering method," J. Appl. Phys. 79, 1244-1249 (1996).
[CrossRef]

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, E. W. V. Stryland, "Sensitive measurement of optical nonlinearities using a single beam," IEEE J. Quantum Electron. 26, 760-769 (1990).
[CrossRef]

Shen, C. Y.

M. J. Moran, C. Y. Shen, and R. L. Carman, "Interferometric measurement of nonlinear refractive-index coefficient relative to CS2 in laser-system related materials," IEEE J. Quantum Electron. 11, 259 (1975).
[CrossRef]

Simos, C.

L. Rodríguez, C. Simos, M. Sylla, O. Marcano, and X. Phu, "New holographic technique for third-order optical properties measurement," Opt. Commun. 247, 453-460 (2005).
[CrossRef]

Smith, P. W.

S. R. Friberg and P. W. Smith, "Nonlinear optical glasses for ultrafast optical switches," IEEE J. Quantum Electron. 23, 2089-2094 (1987).
[CrossRef]

Soileau, M. J.

W. E. Williams, M. J. Soileau, and E. W. V Stryland, "Optical switching and n2 measurements in CS2," Opt. Commun. 50, 256-260 (1984).
[CrossRef]

Song, J. J.

Y. Bae, J. J. Song, and Y.B. Kim, "Photoacustic study of two-photon absorption in hexagonal ZnS," J. Appl. Phys. 53, 615-619 (1982).
[CrossRef]

Stryland, E. W. V

W. E. Williams, M. J. Soileau, and E. W. V Stryland, "Optical switching and n2 measurements in CS2," Opt. Commun. 50, 256-260 (1984).
[CrossRef]

Stryland, E. W. V.

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, E. W. V. Stryland, "Sensitive measurement of optical nonlinearities using a single beam," IEEE J. Quantum Electron. 26, 760-769 (1990).
[CrossRef]

Svetchnikov, V. L.

S. S. Sarkisov, M. J. Curley, E. K. Williams, D. Ila, V. L. Svetchnikov, H. W. Zandbergen, G. A. Zykov, C. Banks, J. -C. Wang, D. B. Poker, and D. K. Hensley, "Nonlinear optical waveguides produced by MeV ion implantation in LiNbO3," Nucl. Instrum. Methods Phys. Res. B,  166-167, 750-757 (2000).
[CrossRef]

Sylla, M.

L. Rodríguez, C. Simos, M. Sylla, O. Marcano, and X. Phu, "New holographic technique for third-order optical properties measurement," Opt. Commun. 247, 453-460 (2005).
[CrossRef]

Tanahashi, I.

I. Tanahashi, Y. Manabe, T. Tohda, S. Sasaki, and A. Nakamura, "Optical nonlinearities of Au/SiO2 composite thin films prepared by a sputtering method," J. Appl. Phys. 79, 1244-1249 (1996).
[CrossRef]

Terhune, R. W.

P. D. Maker and R. W. Terhune, "Study of optical effects due to an induced polarization third order in electric field strength," Phys. Rev. 137, A801-A818 (1965).
[CrossRef]

Tohda, T.

I. Tanahashi, Y. Manabe, T. Tohda, S. Sasaki, and A. Nakamura, "Optical nonlinearities of Au/SiO2 composite thin films prepared by a sputtering method," J. Appl. Phys. 79, 1244-1249 (1996).
[CrossRef]

Torres-Torres, C.

C. Torres-Torres and A. V. Khomenko, "Vectorial self-diffraction of two degenerated waves in media with optical Kerr effect" (in Spanish), Revista Mex. de Física,  51, 162-167 (2005).

Volle, R.

R. Volle, V. Boucher, K. Dorkenoo, R. Chevalier, and X. Phu, "Local polarization state observation and third-order nonlinear susceptibility measurements by self-induced polarization state changes method," Opt. Commun. 182, 443-451 (2000).
[CrossRef]

Wang, H.

Wang, J. -C.

S. S. Sarkisov, M. J. Curley, E. K. Williams, D. Ila, V. L. Svetchnikov, H. W. Zandbergen, G. A. Zykov, C. Banks, J. -C. Wang, D. B. Poker, and D. K. Hensley, "Nonlinear optical waveguides produced by MeV ion implantation in LiNbO3," Nucl. Instrum. Methods Phys. Res. B,  166-167, 750-757 (2000).
[CrossRef]

Wei, T.

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, E. W. V. Stryland, "Sensitive measurement of optical nonlinearities using a single beam," IEEE J. Quantum Electron. 26, 760-769 (1990).
[CrossRef]

Williams, E. K.

S. S. Sarkisov, M. J. Curley, E. K. Williams, D. Ila, V. L. Svetchnikov, H. W. Zandbergen, G. A. Zykov, C. Banks, J. -C. Wang, D. B. Poker, and D. K. Hensley, "Nonlinear optical waveguides produced by MeV ion implantation in LiNbO3," Nucl. Instrum. Methods Phys. Res. B,  166-167, 750-757 (2000).
[CrossRef]

Williams, W. E.

W. E. Williams, M. J. Soileau, and E. W. V Stryland, "Optical switching and n2 measurements in CS2," Opt. Commun. 50, 256-260 (1984).
[CrossRef]

Wise, F.

Wong, G. K. L.

Wong, K. S.

Xiao, R. F.

Yamasaki, S.

Zandbergen, H. W.

S. S. Sarkisov, M. J. Curley, E. K. Williams, D. Ila, V. L. Svetchnikov, H. W. Zandbergen, G. A. Zykov, C. Banks, J. -C. Wang, D. B. Poker, and D. K. Hensley, "Nonlinear optical waveguides produced by MeV ion implantation in LiNbO3," Nucl. Instrum. Methods Phys. Res. B,  166-167, 750-757 (2000).
[CrossRef]

Zykov, G. A.

S. S. Sarkisov, M. J. Curley, E. K. Williams, D. Ila, V. L. Svetchnikov, H. W. Zandbergen, G. A. Zykov, C. Banks, J. -C. Wang, D. B. Poker, and D. K. Hensley, "Nonlinear optical waveguides produced by MeV ion implantation in LiNbO3," Nucl. Instrum. Methods Phys. Res. B,  166-167, 750-757 (2000).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. A (1)

F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, "The optical Kerr effect in small metal particles and metal colloids: The case of gold," Appl. Phys. A 47, 347-357 (1988).
[CrossRef]

IEEE J. Quantum Electron. (4)

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, E. W. V. Stryland, "Sensitive measurement of optical nonlinearities using a single beam," IEEE J. Quantum Electron. 26, 760-769 (1990).
[CrossRef]

S. R. Friberg and P. W. Smith, "Nonlinear optical glasses for ultrafast optical switches," IEEE J. Quantum Electron. 23, 2089-2094 (1987).
[CrossRef]

M. J. Moran, C. Y. Shen, and R. L. Carman, "Interferometric measurement of nonlinear refractive-index coefficient relative to CS2 in laser-system related materials," IEEE J. Quantum Electron. 11, 259 (1975).
[CrossRef]

A. Owyoung, "Ellipse rotation studies in laser host materials," IEEE J. Quantum Electron. 9, 1064-1071 (1973).
[CrossRef]

J. Appl. Phys. (2)

I. Tanahashi, Y. Manabe, T. Tohda, S. Sasaki, and A. Nakamura, "Optical nonlinearities of Au/SiO2 composite thin films prepared by a sputtering method," J. Appl. Phys. 79, 1244-1249 (1996).
[CrossRef]

Y. Bae, J. J. Song, and Y.B. Kim, "Photoacustic study of two-photon absorption in hexagonal ZnS," J. Appl. Phys. 53, 615-619 (1982).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. B (3)

A. Oliver, J. C. Cheang-Wong, J. Roiz, L. Rodríguez-Fernández, J. M. Hernández, A. Crespo-Sosa, E. Muñoz, "Metallic nanoparticle formation in ion-implanted silica after annealing in reducing or oxidizing atmospheres," Nucl. Instrum. Methods Phys. Res. B 191, 333-336 (2002).
[CrossRef]

S. S. Sarkisov, M. J. Curley, E. K. Williams, D. Ila, V. L. Svetchnikov, H. W. Zandbergen, G. A. Zykov, C. Banks, J. -C. Wang, D. B. Poker, and D. K. Hensley, "Nonlinear optical waveguides produced by MeV ion implantation in LiNbO3," Nucl. Instrum. Methods Phys. Res. B,  166-167, 750-757 (2000).
[CrossRef]

J. C. Cheang-Wong, A. Oliver, A. Crespo-Sosa, J. M. Hernández, E. Muñoz, and R. Espejel-Morales, "Dependence of the optical properties on the ion implanted depth profiles in fused quartz after a sequential implantation with Si and Au ions" Nucl. Instrum. Methods Phys. Res. B 161-163, 1058-1063 (2000).
[CrossRef]

Opt. Commun. (3)

R. Volle, V. Boucher, K. Dorkenoo, R. Chevalier, and X. Phu, "Local polarization state observation and third-order nonlinear susceptibility measurements by self-induced polarization state changes method," Opt. Commun. 182, 443-451 (2000).
[CrossRef]

L. Rodríguez, C. Simos, M. Sylla, O. Marcano, and X. Phu, "New holographic technique for third-order optical properties measurement," Opt. Commun. 247, 453-460 (2005).
[CrossRef]

W. E. Williams, M. J. Soileau, and E. W. V Stryland, "Optical switching and n2 measurements in CS2," Opt. Commun. 50, 256-260 (1984).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. (1)

P. D. Maker and R. W. Terhune, "Study of optical effects due to an induced polarization third order in electric field strength," Phys. Rev. 137, A801-A818 (1965).
[CrossRef]

Revista Mex. de Física (1)

C. Torres-Torres and A. V. Khomenko, "Vectorial self-diffraction of two degenerated waves in media with optical Kerr effect" (in Spanish), Revista Mex. de Física,  51, 162-167 (2005).

Other (2)

R. W. Boyd, Nonlinear Optics, (Academic Press, San Diego, 1992).

F. Gonella and Mazzoldi, Handbook of Nanostructured Materials and Nanotechnology (Academic Press, San Diego), Vol. 4 (Optical properties), Chap. 2 (Metal nanoclusters composite glasses), (2000).

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Figures (5)

Fig. 1.
Fig. 1.

Diagram of the propagation vectors of the incident and self-diffracted beams.

Fig. 2.
Fig. 2.

Experimental set up.

Fig. 3.
Fig. 3.

Linear optical absorption of a silica sample containing Au nanoparticles as a function of the wavelength.

Fig. 4.
Fig. 4.

Intensity of I3 as a function of the angle ϕ between planes of polarization of the incident waves.

Fig. 5.
Fig. 5.

Transmitted intensity as a function of the incident intensity in the sample.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

χ ( 3 ) = ( Re χ ( 3 ) ) 2 + ( Im χ ( 3 ) ) 2 .
χ ( 3 ) = n 0 c 7.91 × 10 2 n 2 + i n 0 2 c λ π 2 β ,
E = E + + E ,
n ± n 0 + 2 π n 0 ( A E ± 2 + ( A + B ) E 2 ) ,
E ( x , D ) = T ̂ ( x ) E ( x , 0 ) ,
T ̂ ( x ) = [ exp ( i Ψ + + α ( I ) z 2 ) 0 0 exp ( i Ψ + α ( I ) z 2 ) ] ,
α ( I ) = α 0 + 2 β n ( ε 0 μ 0 ) 1 2 ( E 2 ) ,
Ψ ± ( x ) = Ψ ± ( 0 ) + Ψ ± ( 1 ) cos 2 π x Λ ,
Ψ ± ( 0 ) = 4 π 2 D n 0 λ [ A ( E 1 ± 2 + E 2 ± 2 ) + ( A + B ) ( E 1 2 + E 2 2 ) ] ,
Ψ ± ( 1 ) = 4 π 2 D n 0 λ [ A E 1 ± E 2 ± * + ( A + B ) E 1 E 2 * ] .
E 1 ± ( z ) = [ J 0 ( Ψ ± ( 1 ) ) E 1 ± + i J 1 ( Ψ ± ( 1 ) ) E 2 ± ] exp ( i Ψ ± ( 0 ) + α 0 z 2 + β n ( ε 0 μ 0 ) 1 2 E 2 z )
E 2 ± ( z ) = [ J 0 ( Ψ ± ( 1 ) ) E 2 ± i J 1 ( Ψ ± ( 1 ) ) E 1 ± ] exp ( i Ψ ± ( 0 ) + α 0 z 2 + β n ( ε 0 μ 0 ) 1 2 E 2 z )
E 3 ± ( z ) = [ iJ 1 ( Ψ ± ( 1 ) ) E 1 ± J 2 ( Ψ ± ( 1 ) ) E 2 ± ] exp ( i Ψ ± ( 0 ) + α 0 z 2 + β n ( ε 0 μ 0 ) 1 2 E 2 z )
E 4 ± ( z ) = [ i J 1 ( Ψ ± ( 1 ) ) E 2 ± J 2 ( Ψ ± ( 1 ) ) E 1 ± ] exp ( i Ψ ± ( 0 ) + α 0 z 2 + β n ( ε 0 μ 0 ) 1 2 E 2 z )
I 0 I i = exp [ ( α 0 + β I i ) z ] .

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